Answer:
The solutions are x = 1 and x = -5
Step-by-step explanation:
Hi there!
First, let´s write the equation:
log(3x) + log(x + 4) = log(15)
Apply logarithm property: log(3x) = log(3) + log(x)
log(3) + log(x) + log(x + 4) = log(15)
Substract log(3) from both sides of the equation
log(x) + log(x+4) = log(15) - log(3)
Apply logarithm property: log(15) - log(3) = log(15/3) = log(5)
log(x) + log(x + 4) = log(5)
Apply logarithm property: log(x) + log(x+4) = log(x (x+4)) = log(x² + 4x)
log(x² + 4x) = log(5)
Apply logarithm equality rule: if log(x² + 4x) = log(5), then x² + 4x = 5
x² + 4x = 5
Substract 5 from both sides
x² + 4x - 5 = 0
Using the quadratic formula (a = 1, b = 4, c = -5)
x = 1 and x = -5
The solutions are x = 1 and x = -5
Have a nice day!